N}}f_gP\right)^{(n-1)/2}`, where :math:`n` is the exponent of the
Kennicutt-Schmidt relation (typically :math:`n=1.4`) and :math:`A` is the
normalisation of the law (typically :math:`A=1.515\times10^{-4} {\rm
M_\odot}~{\rm yr^{-1}}~{\rm kpc^{-2}}`). :math:`m_g` is the gas particle mass,
:math:`\gamma` is the adiabatic index, :math:`f_g` the gas fraction of the disk
and :math:`P` the total pressure of the gas including any subgrid turbulent terms.
Once a gas particle has computed its star formation rate, we compute the
probability that this particle turns into a star using :math:`Prob=
\min\left(\frac{\dot{m}_*\Delta t}{m_g},1\right)`. We then draw a random number
and convert the gas particle into a star or not depending on our luck.
The density threshold itself has a metallicity dependence. We use the *smoothed*
metallicty (metal mass fraction) of the gas (See :ref:`EAGLE_chemical_tracers`)
and apply the relation :math:`n^*_{\rm H} = n_{\rm H,norm}\left(\frac{Z_{\rm
smooth}}{Z_0}\right)^{n_{\rm Z}}`, alongside a maximal value. The model is
designed such that star formation threshold decreases with increasing
metallicity. This relationship with the YAML parameters defining it is shown on
the figure below.
.. figure:: EAGLE_SF_Z_dep.svg
:width: 400px
:align: center
...
...
@@ -427,6 +456,15 @@ Star formation: Schaye+2008 modified for EAGLE
does *not* enter the model at all). The values used to produce this
figure are the ones assumed in the reference EAGLE model.
In the EAGLE model, the pressure entering the star formation includes pressure
from the unresolved turbulence. This is modeled in the form of a polytropic
equation of state for the gas :math:`P = P_{\rm
norm}\left(\frac{\rho}{\rho_0}\right)^{\gamma_{\rm eff}}`. For practical reasons,
this relation is expressed in term of densities. Note that unlike the entropy
floor, this is applied at *all* densities and not only above a certain
threshold. This equation of state with the relevant YAML parameters defining it
is shown on the figure below.
.. figure:: EAGLE_SF_EOS.svg
:width: 400px
:align: center
...
...
@@ -442,7 +480,25 @@ Star formation: Schaye+2008 modified for EAGLE
point will also be put on this equation of state when computing its
star formation rate. The values used to produce this figure are the
ones assumed in the reference EAGLE model.
To prevent star formation in non-collapsed objects (for instance at high
redshift when the whole Universe has a density above the threshold), we apply an
over-density criterion. Only gas with a density larger than a multiple of the
critical density for closure can form stars.
Additionally to the pressure-law corresponding to the Kennicutt-Schmidt relation
described, above, we implement a second density threshold above which the slope
of the relationship varies (typically steepens). This is governed by two
additional parameters: the density at which the relation changes and the second
slope. Finally, we optionally use a maximal density above which any gas particle
automatically gets a probability to form a star of 100%.
The code applying this star formation law is located in the directory
``src/star_formation/EAGLE/``. To simplify things, all constants are converted
to the internal system of units upon reading the parameter file.
For a normal EAGLE run, that section of the parameter file reads:
.. code:: YAML
# EAGLE star formation parameters
...
...
@@ -455,13 +511,13 @@ Star formation: Schaye+2008 modified for EAGLE
KS_min_over_density: 57.7 # The over-density above which star-formation is allowed.
KS_high_density_threshold_H_p_cm3: 1e3 # Hydrogen number density above which the Kennicut-Schmidt law changes slope in Hydrogen atoms per cm^3.
KS_high_density_exponent: 2.0 # Slope of the Kennicut-Schmidt law above the high-density threshold.
KS_temperature_margin_dex: 0.5 # Logarithm base 10 of the maximal temperature difference above the EOS allowed to form stars.
KS_max_density_threshold_H_p_cm3: 1e5 # Hydrogen number density above which a particle gets automatically turned into a star in Hydrogen atoms per cm^3.
KS_temperature_margin_dex: 0.5 # (Optional) Logarithm base 10 of the maximal temperature difference above the EOS allowed to form stars.
KS_max_density_threshold_H_p_cm3: 1e5 # (Optional) Hydrogen number density above which a particle gets automatically turned into a star in Hydrogen atoms per cm^3.
threshold_norm_H_p_cm3: 0.1 # Normalisation of the metal-dependant density threshold for star formation in Hydrogen atoms per cm^3.
threshold_Z0: 0.002 # Reference metallicity (metal mass fraction) for the metal-dependant threshold for star formation.
threshold_slope: -0.64 # Slope of the metal-dependant star formation threshold
threshold_max_density_H_p_cm3: 10.0 # Maximal density of the metal-dependant density threshold for star formation in Hydrogen atoms per cm^3.
gas_fraction: 0.1 # The gas fraction used internally by the model.
gas_fraction: 1.0 # (Optional) The gas fraction used internally by the model.
